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AlgebraQ&A LibraryTrue or False? In Exercises 59 and 60, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 59. (a) A 6 × 3 matrix has six rows. (b) Every matrix is row-equivalent to a matrix in row-echelon form. (c) If the row-echelon form of the augmented matrix of a system of linear equations contains the row [1 0 0 0 0], then the original system is inconsistent. (d) A homogeneous system of four linear equations in six variables has infinitely many solutions.Start your trial now! First week only $4.99!*arrow_forward*

Question

True or False? In Exercises 59 and 60, determine

whether each statement is true or false. If a statement

is true, give a reason or cite an appropriate statement

from the text. If a statement is false, provide an example

that shows the statement is not true in all cases or cite an

appropriate statement from the text.

59. (a) A 6 × 3 matrix has six rows.

(b) Every matrix is row-equivalent to a matrix in

row-echelon form.

(c) If the row-echelon form of the augmented matrix

of a system of linear equations contains the row

[1 0 0 0 0], then the original system is inconsistent.

(d) A homogeneous system of four linear equations in

six variables has infinitely many solutions.

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